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If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre. Find the ratio of their radii.
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Verified Answer
$\ell=r_1 \theta=r_1 \times 60 \times \frac{\pi}{180^{\circ}}=\frac{\pi r_1}{3}$
and $\ell=r_2 \theta=r_2 \times 75 \times \frac{\pi}{180^{\circ}}=\frac{5 \pi r_2}{12}$
Since, $\ell$ is same for both the circles
$\Rightarrow \frac{\pi}{3} r_1=\frac{5 \pi}{12} r_2 \Rightarrow r_1: r_2=5: 4$
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